Thu, June 18, 2020
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June 2020
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2:00pm [2:00pm] Claire Voisin (Paris, France)
18 June 2020 (Thursday), 14:00 GMT Speaker: Claire Voisin (Paris, France) Title: Triangle varieties and surface decomposition of hyper-Kahler manifolds Abstract: In recent years, new constructions of complete families of polarized hyper-Kahler manifolds have been found starting from Fano geometry. These hyper-Kahler manifolds also appear as general deformations of Hilbert schemes of K3 surfaces or O'Grady manifolds. I will introduce the notion of surface decomposition for a variety X with a nontrivial Hodge structure on degree 2 cohomology. I will show that this notion is restrictive topologically, as it implies Beauville-Fujiki type relations. I will also show the existence of such a surface decomposition for the general hyper-Kahler manifolds mentioned above. This has interesting consequences on Beauville's conjecture on the Chow ring of hyper-Kahler manifolds. Zoom link: Zoom meeting ID: 991 849 3831 Password: 16-18-June Host: Chenyang Xu

6:00pm [6:00pm] Vivek Mukundan (Unversity of Virginia, USA)
Speaker: Vivek Mukundan (Unversity of Virginia, USA) Day and Time: 6:00 p.m. (18:00 hours), Thursday, June 18, 2020 Title: Two themes on Rees Algebra of Ideals. Abstract: The talk discusses two problems, namely, the Implicitization problem and the stable Harbourne problem which uses Rees Algebra of ideals in an essential way. Implicitization problem seeks the equations defining the closed image of certain rational map. The rational map is defined by a height two perfect ideals satisfying certain conditions. This translates to finding the equations defining the special fiber ring. The second problem relates to finding optimal solution to the containment problem. The containment problem is about finding the best values of n and b such that I^{(b)}\subseteq I^n. We discuss the Harbourne conjecture and various aspects of the containment problem. We then introduce the stable Harbourne problem and prove classes of ideals giving credence to it. Videoconferencing will be via webex. Meeting link: Meeting number: 166 383 6958 Password: pK39MPtDfe3